Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Waals interactions in λ-steps of 0.05.A soft-core Lennard Jones potential was used with a scaling factor of 0.5.The equations of motion were integrated using Langevin dynamics with time-steps of 2 fs.The negative value of the obtained free energy of vaporization, averaged over the 100 repeats, gives the solvation free energy ∆G solv .
From thermodynamic integration, we obtained the value of ∆G solv = -23.45kJ mol −1 for neat (bulk) a99SB-disp water at 300 K and 1 bar.The solvation free energy includes an analytical correction because of the difference in the reference states of the solvated and isolated (in vacuum) water molecules.The standard solvation free energy (and the standard enthalpy of vaporization etc.) describes the transfer of the solute (here, a water molecule) from a thermodynamic standard state of the gas (ideal gas at 1 bar) to the thermodynamic standard state in solution (ideal solution at 1 mol L −1 ).This includes a change in concentration from 1 bar (that is, 1 mol per 24.94 L at 300 K) to 1 mol L −1 , which is not included in the TI calculation.The correction term is w = − .023 kJ mol −1 and the corrected solvation free energy is ∆G solv = -31.47kJ mol −1 .Hence, the vaporization free energy ∆G vap = 31.47kJ mol −1 .
The vaporization enthalpy is given by ∆H vap = −E pot + RT , where E pot is the average interaction energy of a water molecule with its surrounding in bulk water.The obtained E pot from the simulation at a99SB-disp water is -52.53 kJ mol −1 .Since the water model used has fixed point charges, this potential energy needs to be corrected for the self-polarization, The entropy of water is thus obtained as S = (∆H vap − ∆G vap )/T .The entropy at 300 K is 54.4 J mol −1 K −1 , in excellent agreement with the 2PT entropy of 54.7 J mol −1 K −1 .

Tables for changes in water population and thermodynamic quantities
This section tabulates the data plotted in Figures 4, 7 2α.The magnitude of the dipole moment of the a99SB-disp water model is µ = 2.44 D and the dipole moment of a water in vacuum is µ 0 = 1.85 D. With 1 D = 3.33 × 10 −30 C•m and the polarizability of water of α = 1.608 × 10 −40 F•m, one obtains ∆E pol = 7.23 kJ mol −1 .Hence the corrected energy per water molecule is -45.30kJ mol −1 and with RT = 2.48 kJ mol −1 one obtains ∆H vap = 47.78 kJ mol −1 .

Table 1 :
, and 8 in the main text.See also Change in number of water molecules per protein.

Table 4 :
Change in water-water energy.

Table 8 :
Change in protein-protein energy.